Viscocapillary lift force near a fluid interface

The force exerted on an object moving in a viscous fluid, and its modification induced by the presence of a nearby boundary, have been abundantly studied in fluid mechanics for the past century. In the last decades, soft gels and elastomers have been of growing interest, and have been shown to break the symmetry of nearby low-Reynolds-number flows, thus generating a force normal to the substrate. Such a lift force depends in particular on the material properties of the substrate and the intervening fluid. Here, we revisit this problem, by addressing the novel situation where the soft substrate is replaced by a fluid interface. We analyze in details the lubrication flow between a moving object and the interface. Using a combination of analytical and numerical treatments, we derive an expression of the viscocapillary lift force at leading order in compliance.